a: \(\left(10^2+11^2+12^2\right):\left(13^2+14^2\right)\)

\(=\frac{100+121+144}{169+196}=\frac{365}{365}=1\)

b: \(1\cdot2\cdot3\cdot\ldots\cdot9-1\cdot2\cdot3\cdot\ldots\cdot8-1\cdot2\cdot3\cdot\ldots\cdot7\cdot8^2\)

\(=1\cdot2\cdot3\cdot\ldots\cdot8\cdot\left(9-1-8\right)\)

=0

c: \(\frac{\left(3\cdot4\cdot2^{16}\right)^2}{11\cdot2^{13}\cdot4^{11}-16^9}=\frac{\left(3\cdot2^{18}\right)^2}{11\cdot2^{13}\cdot2^{22}-2^{36}}=\frac{3^2\cdot2^{36}}{2^{35}\cdot\left(11-2\right)}=2\)

d: 1152-(374+1152)+(-65+374)

=1152-374-1152-65+374

=-65

\(\frac{\left(3.4.2^{16}\right)^2}{11.2^{13}.4^{11}-16^9}\)

\(=\frac{3^2.4^2.2^{32}}{11.2^{13}.2^{22}-2^{36}}\)

\(=\frac{3^2.2^4.2^{32}}{11.2^{35}-2^{35}.2}\)

\(=\frac{3^2.2^{36}}{2^{35}.\left(11-2\right)}\)

\(=\frac{9.2^{35}.2}{2^{35}.9}\)

\(=2\)

\(\frac{\left(3.4.2^{16}\right)^2}{11.2^{13}.4^{11}-16^9}\)

= \(\frac{3^2.4^2.2^{32}}{11.2^{13}.2^{22}-2^{36}}\)

= \(\frac{3^2.4^2.2^{32}}{11.2^{35}-2^{35}.2}\)

= \(\frac{3^2.2^4.2^{32}}{2^{35}.\left(11-2\right)}\)

= \(\frac{3^2.2^{36}}{2^{35}.9}\)

= \(\frac{9.2^{35}.2}{2^{35}.9}\)

= \(2\)

\(B=\dfrac{3^2.4^2.2^{18}}{11.2^{13}.2^{22}-2^{36}}\)

\(B=\dfrac{3^2.2^{22}}{2^{35}\left(11-2\right)}\)

\(B=\dfrac{3^2}{2^{13}.9}\)

\(B=\dfrac{1}{2^{13}}=\dfrac{1}{8129}\)

= 3^2 . 2^4 . 2^32 / 11.2^13 .2^22 - 2^36

=3^2 . 2^36 / 11.2^35 - 2^36

=3^2 . 2^36 / 2^35 . ( 11+2)

= 9 . 2^36 / 2^35 . 13 

= 9 . 2 / 13 = 18/13

\(\frac{\left(3.4.2^{16}\right)^2}{11.2^{13}.4^{11}-16^9}=\frac{3^2.2^4.2^{32}}{11.2^{13}.2^{22}-2^{36}}=\frac{3^2.2^{36}}{11.2^{35}-2^{36}}=\frac{2^{35}\left(9+2\right)}{2^{35}\left(11-2\right)}=\frac{11}{9}\)

Help me

\(\frac{\left(3.4.2^{16}\right)^2}{11.2^{13}.4^{11}-16^9}\)

\(=\frac{3^2.2^{36}}{11.2^{34}-2^{36}}\)

\(=\frac{3^2.2^{36}}{2^{34}.\left(11-2^2\right)}\)

\(=\frac{9.2^{36}}{2^{34}.7}\)

\(=\frac{36}{7}\)